The correct answer is $14$ . It's given that a number $x$ is at most $2$ less than $3$ times the value of $y$. Therefore, $x$ is less than or equal to $2$ less than $3$ times the value of $y$. The expression $3y$ represents $3$ times the value of $y$. The expression $3y-2$ represents $2$ less than $3$ times the value of $y$. Therefore, $x$ is less than or equal to $3y-2$. This can be shown by the inequality $x≤3y-2$. Substituting $-4$  for $y$ in this inequality yields $x≤3(-4)-2$ or, $x≤-14$. Therefore, if the value of $y$ is $-4$. the greatest possible value of $x$ is $-14$.